196 
MR. LLOYD ON THE DIFFERENCE OF LEVEL BETWEEN 
and eleventh the distance in feet from staff to instrument and instrument to 
staff ; the fourth and twelfth the correction for the curvature of the earth ; the 
fifth and thirteenth the mean observations minus the curvature ; the sixth and 
eighth are the length of the bubble and the thermometer attached to the 
instrument. This last is useful as a check to the bubble, which, when the 
instrument is moved suddenly, shakes into several small globules, that some- 
times do not immediately unite again : this is detected by the length of the 
bubble, which ought to correspond to a certain degree of the thermometer. 
Column fourteen is the difference between columns five and thirteen ; column 
fifteen is that difference + or — ; and column sixteen is the amount of that 
difference added or subtracted, according to the sign, from the former quan- 
tity. These quantities are a continuation of heights above or below the first 
picket, or the northern standard in the dock-yard at Sheerness. 
In order to prove the correctness of the different columns, they are summed 
up at the bottom, when the gross sum for curvature, being deducted from the 
gross sum of columns two and eleven, show the correctness of columns five 
and thirteen ; and the difference between the sums of columns five and thirteen 
+ or — , added to or subtracted from the little figures above the top line in 
column fifteen, ought to give the last true level in column sixteen at the bottom 
of the page. 
The whole is further proved by taking the sums of columns five and thirteen 
of each page, and the difference of the whole amount of each gives a proof of 
the correctness of the whole work, by giving the difference at once between 
picket 1 and 445. 
The same method is pursued in the proof-levels up to No. 112 : after that, 
all the corrections become reversed, the curvature being additive (as the com- 
plement to 10,000 is read off on the staff). The difference between the proof- 
levels continue from standard at Sheerness to New London Bridge, and will 
be found to be 0.0110, and varying at different distances from Sheerness, but 
never more than 0.0300. 
As there is not, in any work that I have seen, a correct table of curvatures 
of the earth for small distances, I have added one for every five feet from 60 
to 1000. 
